#519 Barrie May: “If you want to do something, why not sign a petition here at the Whitehouse website: http://wh.gov/k10u”

I’m a German, so influencing an U.S. petition doesn’t seem right.

I’m doing a lot of things. For a long time I was happy to just reduce my own private CO2 footprint, but somehow this has changed. I’m currently seeking ideas how to do something on a political level, I just don’t know yet.

It’s an animated GIF file that shows global-average temperature results computed from randomly chosen rural stations, starting with one station and then incrementing one station at a time up to 40 stations. Just click on the link and watch the animation in your browser. In the upper plot, raw data results are shown in red, homogenized data results in green, and the official NASA/GISS “meteorological stations” results (for reference purposes) in dark blue.

The lower plot shows how many of the selected stations reported data for any given year (one month is counted as 1/12 year). The #selected stations is shown in the upper-right corner of that plot (goes from 1 to 40).

Stations were pre-screened only for adequate data record length (i.e. stations with data going back to 1885 or earlier or with data from 2010 or later) to ensure decent global coverage from 1885 to the present.

521 Jim Larsen: “It matters not whether the poor household is in the USA or Yemen. The price of carbon is the price of carbon.”

As far as I can see this is the concept also advocated by James Hansen. And it seems to be the best that I understood.

However: As soon as carbon gets a price and the money is returned to the public, this will raise the price of many goods and at the same time the ability of most people to pay that price, that sounds to me like inflation.

If a good is produced in one country, let’s say China, then the CO2 price is to be paid to the Chinese Government and they will return it to the Chinese people. However if the good is sold to let’s say Germany, then the German customer will have to pay, together with the price for the good, the carbon emission price that is later returned to the Chinese citizens. I think this will likely cause an important value transfer.

However I don’t understand the consequences of this for the currency exchange rates. The price for CO2 in USA is not the same as the price for CO2 in Yemen, for the former is in Dollar and the latter is in Rial. I cannot understand how exchange rates will be influenced when trading goods created under a CO2 emission tax.

It also depends on when CO2 taxes are charged. James Hasen suggested to charge as early as possible, so usually when oil is extracted from the ground and first sold. That would mean it is charged for example to a Russian company that produces the natural gas. What will the Russian government do with that money?

The EU started a CO2 emissions trade for flights this year. 10 % of emissions for flights have to be bought for every plane starting or landing in the EU. China prohibits it’s airlines to follow these EU laws.

I can’t understand why that is a sensible definition of a runaway feedback effect, or why that ends up “putting things completely out of our control” (as if once the methane starts going up, let’s just give up and burn all the coal because it won’t matter anyway).

In any case, the lay reader is left with the impression that such a scenario would be absolutely catastrophic, and that once Arctic methane sources exceed human CO2 sources (using this rather arbitrary criteria) what we do won’t matter anymore. He also gives the distinct impression that the majority of the scientific community thinks this is a plausible scenario, and without any reference to the relevant uncertainties and timescales. There’s really no justification for this type of video.

Finally, it’s quite common in science to criticize other people’s science without implying that they are cranks or have no credibility. I realize that blogs typically argue on the far fringes of the debate, and constructive criticism is often lost, but I don’t know of Steven Chu’s work, and have made no implication about him as a scientist. I’ve also criticized Jim Hansen’s version of the “runaway greenhouse” that he has outlined in his book. This is not incompatible with acknowledging him as one of the best climate scientists of our time.

re Jim Larsen – 538 (re me), 547 (Jevon’s?), 545 (scale re Secular Animist), Secular Animist 542 (re Dan H. 541),
– I should probably clarify that specifically what I meant was that it should tend to be more efficient to choose building a unit of clean energy infrastructure in a developing country than replace a unit of dirty energy infrastructure with said unit of clean energy infrastructure while building another new dirty energy infrastructure unit; of course those aren’t the only two choices. I am aware that such policies as CDM for emissions offsets can run into trouble; it has also been said not to let perfect be the enemy of good (also keep in mind when dealing with trade, Jevon’s, tariffs/subsidies, etc.). Maybe the rich nation seeking an offset could offer to pay the difference between clean and dirty so that it isn’t simply building new infrastructure with no (simple direct) impact on emissions trajectories, although that seems stingy somehow. But as has been pointed out we shouldn’t get too far into this here. This may be a more proper venue http://scienceblogs.com/stoat/2012/06/25/carbon-tax-watch/ , although …? (Rabett Run is also fairly wide-ranging in subject matter).
– interesting point (regarding near subsistence-level clean energy): solar ovens. saw a presentation once about that. some culture(s?) don’t like it, due to it’s taking away the act of firewood gathering, in so doing takes away women’s socializing time.

re Dan H. 541 – that’s what I meant by human population dynamics being “fortunately complex” – that it helps to control our population growth by being nice to each other (in specific ways), as opposed to how we would control deer or lady bugs (or aphids) or gypsy moths, etc. (would that change if deer reached a stage part-way between subsistence and affluence? Well…). But I don’t think this requires achieving the same level of wealth, if the methods are chosen well; and also, pursuit of population stabilization may achieve greater wealth as a byproduct and/or knock-on effect, which is a good reason for pursuing it. Maybe you can find out some details googling this topic along with Gates Foundation.

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re Bernd Herd 540 – thanks for the explanation of the EEG. Although I think su bs idi es, l o a n gu ar ant e es (I’m not taking chances on the spam filter), and building codes, etc, shouldn’t be avoided, an across-the-board global-constant emissions tax should tend to be an efficient, fair solution and perhaps make all the rest run more smoothly (as well as provide funds where necessary). For fossil fuels I’m partial to taxing at the well/mine, (although with some tax deduction for products that contain fossil C, proportional to the likelihood and extent that they won’t be oxidized in the foreseeable future). It may be harder to assess the tax for other sources (but see above on perfect being the enemy of the good).

For elaboration see my 531, the comments mentioned within that and links therein – in particular, my comments at the Stoat link above andhttp://skepticalscience.net/glimmer_of_hope_a_conservative_tackles_climate.html#81289
(I had previously posted an earlier link to those comments but that link no longer works).
But a quick summary of some of my thoughts: I think a case can be made for some combination of equal per-capita payback and tax reduction, but the rationale for this must be that this somehow compensates for the costs of global warming or adaptation to that; as much of this occurs in the future (with different people), this is private sector economic investment to boost the economy now so that it may make itself more robust in the future (?). I don’t think it should all go back to the private sector so directly. Internationally, nations or groups of nations with varying policies could enact tariffs and subsidies (proportional to embodied emissions and international policy differences) for trade. I would like to think that as much as such unilateral actions may be hard for the nations taking them, they may also pull other nations along – an incentive for other nations to join in to some extent, perhaps allowing a global tax rate of sorts to grow from the bottome up. And… no I really shouldn’t try to fit anything else here.
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re 546 wili – regarding your last paragraph, I get the sense that skeptical science was saying (links in my 446 for anyone wondering) that the permafrost feedback, as modelled by the paper (MacDougall et al), was not a ‘Chuvian’ runaway. Another way of putting it: Just like H2O (outside runaway), the C gain by the atmosphere from C loss from permafrost ‘penultimately’ reaches an equilibrium value that varies as a continuous function of the imposed forcing, rather than having a discontinuous jump. But it reacts more slowly than H2O – acting more slowly than much of the rest of the climate system.

re 535 Chris Colose – thanks; I should clarify that in 533, I meant something along the lines of ‘hypothetically’ when I wrote ‘concievably’, as in, if the other feedbacks individually were positive and large enough.

CH4 – yes, the rate at which, as a feedback, a C reservoir is depleted with some fraction going into the atmosphere would be relatively more impotant if more of it is as CH4; if Chuvian runaway (thanks, wili) can be achieved, to the point of exhausting some (designated portion of a) surface C reservoir, with a CH4 flux, then there would be a cooling period afterword (setting aside other slow feedbacks), and if the CH4 feedback were slowed down, then the feedback wouldn’t be as strong, and perhaps the C reservoir wouldn’t be exhausted unless the external forcing were larger (this being a hypothetical discussion; no assertion that it will happen).

I don’t believe the conversation was getting into the territory where CH4 saturation (to the point that it becomes weaker than CO2 on a per molecule basis) becomes an issue.

I think it makes sense to note that any discontinuous step in equilibrium climate as a function of forcing represents some runaway, even if it is small – it doesn’t always have to refer to a snowball or steamball situation, although at some point it becomes trivial, masked by noise, the butterfly effect, error bars, etc. That you can’t have half a H2O or CO2 molecule in the atmosphere would technically imply that any H2O or CO2 feedback consists of trillions of trillions of … little tiny runaways (with low sensitivity in between), but it’s not necessary or generally helpful to think of it like that, merely interesting.

I agree with wili that Chu seemed to be refering to such a Chuvian runaway and not the big ones of snowballs and steamballs (or at least it makes sense to infer that).
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re 508 Chris Korda – wow, an inductor is a good analogy for the effect of heat capacity (where applied voltage is the forcing and current is the temperature; http://en.wikipedia.org/wiki/Inductor : v = L*di/dt … um, we still need a resistor … but I may have been mistaken when I told Bobl back in August that a circuit wasn’t a good analogy. Oops.

re my “an incentive for other nations to join in to some extent” – by way of trade, but also, by the stipulation that nations only recieve international climate (and acidification) adapatation funds if and proportional to their tax rates.

re 558 Bernd Herd – a domestic CO2 tax would apply as a tariff to fossil fuel imports (from nations without such a carbon price, or from nations with a carbon price that is applied at the point of combustion rather than the well. Etc. Such nations might choose to tax their fossil fuel exports so that they can get that revenue for themselves – fine).

I think the inflation would be a consequence of that fact that (except for some things), in so far as the efficient market hypothesis applies, we would be operating optimally now except for global warming and ocean acidification; applying the tax pulls us away from that optimum, the economy will then not be as efficient (ignoring externalities); but we should want to do this because the economy is now more efficient when including the externalities.

558 Bernd said, “That would mean it is charged for example to a Russian company that produces the natural gas. What will the Russian government do with that money?”

Uh, why would the Russian government get the money at all? Global problems, such as CO2, require either a global government, or a virtual global government as can be provided by treaties. You provided a grand example – giving countries carbon allowances based on population. (I’d probably twist it by setting current population in stone, as adjusted by immigration and emigration. If you drop your population, you get the benefit. Raise it, and pay your own way.) The major players in world economics can easily force all others to sign whatever they choose by using the threat of economic isolation. Even Iran, rich beyond belief with oil, is straining under sanctions. “But why would the major players insist on saving the world, when that would be less profitable for the major players (though wildly more profitable for humanity)?” Yep, that’s the question you brought up, and it’s the $64,000 question.

The apparent great Arctic sea ice refreeze as some “fake skeptics” put it, is bunk. It is rather better to let them indulge in their own fantasies.

What is really happening is almost science fiction, was it not observed otherwise, but new Arctic weather features surprise with consistent warmer temperatures. First, Arctic snow showers in really calm winds cover wide expanses of the sea surface, help tame the colder than 0 C sea water, the flakes almost float but gather in clusters extending large areas. Unlike the suspended snow found a little under sea surface, grey ice ideally spreads quickly on top if the temperatures are right. this happens with Sea surface temperature of -1.8 C and surface air temperatures of about -11 C , this -11 C has just been reconfirmed once again. At Warmer than -11 sea ice did not form. A quick refreeze wouldn’t require air temperatures so cold, the onset of winter cold enough to make sea ice has also been delayed. This is recognized by a feature found in temperature upper air profiles, where as the maxima in temperature shifts from the ground
to several hundred meters above. Boundary layers came with the formation of sea ice. For North of Barrow Strait 95 W this date was October 18 for 2012, it was: september 26 for 2011, september 23 for 2010, September 18 – 2009, September 14 – 2008 and October 5 for 2007. Signs for a strong winter would have meant that profiles with upper inversions show strong by early september. The arrival of upper inversions coincided with the expanding great Arctic sea ice boundary, this should be the same everywhere else. When snow stays over land so would intense upper air inversions much warmer than the surface. For all practical purposes this years refreeze has been latest in the last 6 warmer than normal years. Some evidence presented http://eh2r.blogspot.ca/

Chris Dudley @524: I was going to make a stove analogy myself but you beat me to it. To model your electric burner case, I did another test run with hacked data, this time adding a trianglar burst instead of a square burst. Here’s a plot of the input CO2 concentrations, and here’s a plot of the output temperatures. Note that at the peak of the forcing, the instantaneous response also peaks, but the Climate Response Functions continue to rise. I shut off the electric burner, and the burner starts to cool, but the water continues to warm, just as you say should be the case.

553 Bernd, the study says, “and b is the proportion of the global E available to a group. We divided the global population into the developed and the developing world because of the large imbalance in energy use between them” … “thus, b is 0.85 in the developed world and 0.15 in the developing world.”

Truly an abysmal assumption that ruins the paper. Our energy use will certainly decline, leaving a larger and larger share of the energy pie to the developing world.

564 SecularA said, “The “problem” will be “solved” long before that, by famine, water scarcity, disease and war.”

I take it you’re not feeling optimistic today.

573 Ray L said, “If that is the case, then we are screwed.”

Maybe, and you’re right about mankind’s provincial nature. But global temperatures should spike soon as natural variability inevitably returns to median or even hot. This likely event will undermine essentially all skeptic arguments by showing the last decade wasn’t a peak but a pause. Arctic sea ice could very well continue to decay, which will supply big planetary scale. And drought in the US might return each year for a while, making things personal.

If all of these happen to happen for the next ~4 years, then people might see an existential threat. Therein lies hope.

There’s a nice example. And there is some lag there. So, should the water start to cool while the burner is still warmer than the water? If we take the yellow line (instantaneous) as the burner, all the other lines start cooling before they intercept the yellow line and that is what is bothering me. They should not start to cool before the intercepts. I have still not found the details for the model run that produced fig. 7 in Hansen et al. (2011) but I have looked at some 100 year responses to 2x, 4x, and 8x carbon at the GISS web site and I am thinking that I am on the right track in clearing up this itch: The climate response function gives us a way to calculate the average temperature given a forcing without doing a whole model run for that. But it does not give us separate information about sea surface temperature and land surface air temperature. But, if we were to put a styrofoam cup of water into our pot of water, turn the electric burner on and then turn it off, we might get an average temperature for the water in the cup and the water it floats in that behaves as your calculation does. The water outside the cup would not start to cool until the burner got to the temperature of that water, but the average temperature would never get to that high a temperature.

Off to the races indeed. Yesterday the Arctic sea ice extent reached 6433281 sq km and achieved the highest seven day recovery rate of the last eleven years. It is a little like that old Vonnegut story Ice-nine.

Jim Larsen wrote: “Global problems, such as CO2, require either a global government, or a virtual global government as can be provided by treaties.”

At present, the most aggressive and effective governmental actions to reduce GHG emissions are being taken at the level of national (Germany), state (California) and even municipal governments. So it’s not at all clear that solving the GHG emission problem “requires” a “global government”.

re my 529 “The vapor pressure in equilibrium with supercooled droplets (liquid H2O) is higher than that in equilibrium with solid H2O at the same temperature” – pure water, flat surfaces; can be true for impure water with other surfaces as it would be in real clouds but there may be some adjustments (Wallace and Hobbs, “Atmospheric Science – An Introductory Survey” – pp 72-73 specifies flat surface for the ice as well)

Chris Dudley @561: Here’s a graph that combines the two graphs I posted @571. The additional pink triangle is the input data. Since it’s in ppm CO2 not degrees, the y-scale is inappropriate, but the x-scale is correct. The pink triangle represents the forcing, and should therefore be the burner in your analogy no? Even the instantaneous response is non-linear in y, due to the log relationship of temperature to forcing.

@524 you said:

You shut it off and the burner starts to cool, but as long as it is hotter than the water, the water should still warm. And that does not happen in your calculation. The water starts to cool while the burner is still hot.

I think the triangle burst graph above says otherwise. The pink curve (the forcing AKA the burner) peaks in 2066, but the red curve continues rising due to hysteresis, and doesn’t peak until 2068.

I don’t claim to have exactly reproduced Hansen’s fig. 7, which would be tough to do since he doesn’t give source code. Nor am I explicitly using Green’s function. I’m using derivatives, the effect of which may be equivalent to using Green’s function. Perhaps it would help if I explained my method in more detail?

Re 583 Chris Korda – having looked at the graph, setting aside the effect of varying response times of different parts of the system as suggested by Chris Dudley (if I’m remembering correctly), one would expect all heat-capacity-delayed responses to always be approaching the instantaneous (zero heat capacity) response, which is why their slopes should change sign when they intersect the instantaneous curves. (The difference between zero and non-zero heat capacity responses is proportional to a radiative imbalance, which is proportional to the rate of change in enthalpy and thus temperature, barring a change in where the heat is going, etc.)

It is the forcing that is logarithmic in concentration. T comes right from the forcing and sensitivity: 3/4 degree C per (Watt per square meter). That is why I’m taking your yellow line as the forcing.

So, again, if the yellow line is what we’d get with no delay, then it should be the target temperature for any lagged response. If the lagged temperature is moving away from the target rather than towards it then there needs to be an explanation as to why.

I’m guessing you are implementing eqn. 3 of Hansen et al. to calculate the lag?

#579 SecularAnimist: “At present, the most aggressive and effective governmental actions to reduce GHG emissions are being taken at the level of national (Germany), state (California) and even municipal governments. So it’s not at all clear that solving the GHG emission problem “requires” a “global government”.

I don’t think that local actions will be sufficient. They are some start, but in the end they cannot be sufficient. The more oil and gas we save on our own initiative, the less the world-wide oil and gas prices are going to rise and the oil and gas saved now is going to be consumed a few months later by somebody else.

To save the amount of CO2 that a friend wastes for his summer holidays, I’d have to leave my house could for a whole winter. It just cannot work.

Remember that huge known reserves in coal, gas and oil will have to stay unused forever, not just for a few more months.

We absolutely need globally organized actions. And I currently think they will likely be game changers, for I have no idea how to reach the goal without changing the game. Should we pay for the Yasuni-Initiative? http://en.wikipedia.org/wiki/Yasuní-ITT_Initiative

579 SecularA said, “At present, the most aggressive and effective governmental actions to reduce GHG emissions are being taken at the level of national (Germany), state (California) and even municipal governments. So it’s not at all clear that solving the GHG emission problem “requires” a “global government”.”

You’re touching on actuarial concepts. Would you agree that “success” could be defined as an 85%+ rate of compliance? I don’t see how you’re going to get that in a voluntary system where any success will drastically increase the financial reward of non-compliance. Cheap natural gas? Lots of folks will up the thermostat a bit this winter. Drop oil to $30 a barrel and watch those SUVs sell…

“I don’t claim to have exactly reproduced Hansen’s fig. 7, which would be tough to do since he doesn’t give source code.”

We should be careful here since that is a denier types statement. You can get the source code for the model. You’d have to run it though, and you would not get exactly the same curve. I was poking around for the detailed output of the run fig. 7. was based on (3000 year simulation) and have not found it yet.

Yasuni sounds nutso. I believe one of the links said that we’ve already got 5 times the reserves needed to exceed rational emissions and we’re still looking for more. So we’d have to spend 80% of gawdaful sums before getting a single barrel’s worth of remediation, Carbonwise, why do we care where the next well gets drilled?

Perhaps… Tell the current producers they’ll get a global monopoly at, say $50 a barrel. We require consuming nations charge a $50 a barrel tax. Make both rise in step over time. Add complexity without gamemanship, The US, Europe, China, and Japan have plenty of economic and military power to make such a decision stick.

Chris Dudley: I think confusion may be arising over use of the word “lag”, by which I understand you to mean time delay. My model exhibits smoothing, which includes but is not limited to time delay. Hence my model can temporarily move in the opposite direction of the instantaneous response, depending on how quickly the input changes direction, but given sufficient time and input stability it will eventually move in the same direction as the input. I’m not claiming this is or isn’t a realistic numerical model of climate response, I’m just trying to accurately describe how the model works.

I’m not sure what you mean about figure 3. I’m using the Climate Response Functions given in figure 5, which I implemented as polylines in log space, similar to envelopes in acoustics. Assuming the CRFs are already interpolated, my method can be broken into two steps. The first step uses derivatives to model inertia, resulting in smoothing (and time delay) of the input signal, as follows:

For each yearly CO2 concentration delta, slice that delta into 2,000 portions of unequal (decreasing) size, one portion for each of the next 2,000 years, according to the percentages specified by whichever CRF we’re using. For the “intermediate” CRF the percentages are yr1=15%, yr2=24%, yr3=29%, yr4=33%, etc. So the CRF percentage deltas are 15%, 9%, 5%, 4%, etc. Suppose the first CO2 delta is +10ppm, for the year 1750 (not realistic!) The concentration delta slices (distributed over the next 2,000 years) are therefore 1.5, 0.9, 0.5, 0.4, etc., so we add 1.5 to 1750’s concentration “bucket”, 0.9 to 1751’s bucket, 0.5 to 1752’s bucket, etc. After the first pass the buckets contain:

year 1750 1751 1752 1753 ...
dCon 1.50 0.90 0.50 0.40 ...

Now suppose 1751’s CO2 delta is double 1750’s or +20ppm. This time the concentration delta slices are 3, 1.8, 1, 0.8, etc., so we add 3 to 1751’s bucket, 1.8 to 1752’s bucket, 1 to 1753’s bucket, etc. After the second pass the buckets contain:

year 1750 1751 1752 1753 ...
dCon 1.50 3.90 2.30 1.40 ...

Note that for each pass, the 2,000 year window moves forward a year, so on the second pass we’re adding to the buckets for 1751..3751 instead of 1750..3750. This process is repeated for all the input CO2 concentration deltas. Once this first step is completed, our buckets contain the smoothed CO2 concentration deltas for the entire model run.

The second (much simpler) step is: for each bucket, compute the smoothed absolute CO2 concentration for each year (by doing a running sum of the buckets), and feed each yearly smoothed absolute concentration to the instantaneous equation: log(ppmCO2) / log(2) * 3, yielding temperature increase relative to baseline for that year. That’s my numerical model of thermal inertia FWIW.

Kevin M at #554–The first effect of trees in the tundra will be to increase local warming because of change of albedo. Longer term, it would have to be a very tall, thick forest to contain the quantities of carbon now in the permafrost. In some places, the permafrost is nearly a mile thick. I hate to go to wikipedia, but they seem to be well sourced here:

“The most recent work investigating the permafrost carbon pool size estimates that 1400–1700 Gt of carbon is stored in permafrost soils worldwide.[1] This large carbon pool represents more carbon than currently exists in all living things and twice as much carbon as exists in the atmosphere.”

Chris C. at #560: Thanks for another thoughtful reply. Please note that neither I nor Chu (nor anyone else that I’ve seen, besides you) has said anything like “let’s just give up and burn all the coal.”

I’m just trying to figure out where we are along in terms of tipping points and feedbacks. I happen to agree with Secular Animist and others that we need to cut CO2 and other ghg emissions to as close to zero as quickly as possible at thsi point no matter what further bad news from science comes along wrt said tipping points and feedbacks. But I still think it is important to understand what the latest science is telling us, including consequences implied but not explicitly spelled out. I kind of assumed that this is exactly what a blog like this is intended to do, but I would be happy to be corrected.

You seem to think of the point when feedbacks exceed human forcing is just an arbitrary point. Chu and many others don’t. Perhaps we should leave it there as a difference of evaluation of relevance of this point. I actually think it could be the wake up call we have been hoping for–that as people really understand the consequences, it will be a global “Oh sh!t” moment (tamino’s term, following kate’s statement at ClimateSight) that will shock people into scaling way back on emissions at once and working harder to create systems that allow human (and non-) well being without resort to burning fossil (better called “death”) fuels.

For the record, I have given up flying (and all ff-powered long-distance travel), most driving and meat eating…and have worked on every level (family, work, municipal, state, national, international–though the last I mostly leave to my bro who, as head of a major international NGO, is better positioned to influence international entities) to push them to move rapidly to low or no emissions and low or no emissions waste, and at great risk to relationships and to my professional career. This all to just to say that I am certainly not looking for an excuse to just “just give up and burn all the coal.”

Thanks again to all for engaging in discussion of this important study and its implications. I’ve been particularly impressed by and thankful for your excellent writing and analysis here and elsewhere, Chris C.

Jim Larsen: “Global problems, such as CO2, require either a global government, or a virtual global government as can be provided by treaties.”

As Ray Ladbury said, no chance of that yet. The nation-state political model is still well-entrenched, despite the fact that corporations and the megarich have already moved on from it. In fact it serves their interests not to have a new political and diplomatic model, and the UN only passes for one.

It may be that AGW will shake things up but not before it becomes all too evident and immediate.

wili @594: “shock people into scaling way back on emissions” For a shock, look no further than the latest tar sands aerial photos from Ashley Cooper. Not for the faint of heart. The sulfur mountains are bizarre, like something from an alien civilization.

I should have spelled that out. I meant equation 3. in Hansen et al. not figure 3. If you look at that you’ll see that the CRF is applied to the derivative of the forcing, not the derivative of the concentration. You need to take the log sooner I think.